In ∆lmn,mn is extended to o.if angle mln=100-x,angel lmn =2x and angeleno=6x-5,find the value of x
Answers
If angle mln=100-x,angel lmn =2x and angle lno=6x-5, then the value of x is 21°.
Step-by-step explanation:
It is given,
∠mln = [100-x]
∠lmn = [2x]
∠lno = [6x-5]
From the figure attached below we have
∠lnm + ∠lno = 180° …… [strainght line]
⇒ ∠lnm = 180° - [6x - 5] = 180° - [6x - 5]
⇒ ∠lnm = 180° - 6x + 5
Now, using the angle sum property in ∆lmn, we get
∠mln + ∠lmn + ∠lnm = 180°
⇒ [100-x] + [2x] + [180° - 6x + 5] = 180° ..... [substituting the above values]
⇒ 5x = 100 + 5
⇒ x = 105/5
⇒ x = 21°
Thus, the value of x is 21°.
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